With precise predictions, as opposed to expectations, you could time the market. Alas, I don’t have precise predictions. If I could predict the Dow, I wouldn’t be writing this essay. I would be on a yacht trading options.

Expectations are still useful, though. They do two things. First, they tell you where to put most of your long-term money. Since the expectation is higher on stocks than high-quality bonds (see below), youngsters investing for the year 2059 should be in stocks. They can weather the occasional 50% crashes that will interrupt this century’s bull market.

Sculpture by Brian Hoag

Forbes

The other thing an expectation can do is inject some realism into your life. The expected return on stocks is much lower than the historical return on stocks. This may mean that your retirement plan is hopelessly out of date and that you should increase your saving.

If “expect” does not mean “predict,” what does it mean?

Suppose you put $2 down on a roll of dice, with your payoff $100 for throwing boxcars (a pair of sixes) and nothing for any other pair. Then your expected payoff is $2.78. Meaning: If you played this game 10,000 times, at a cost of $20,000, your winnings would probably be close to $27,800. So your expectation from one throw is $2.78. That’s a 39% expected return.

Sculpture by Brian Hoag

Forbes

In this game $2.78 is not a prediction of what will come with one throw. You know that won’t happen; the only possible outcome is either zero or $100. But $2.78, the expected payoff, does tell you whether to play the game.

Some people form their expectations by extrapolating past returns. This is profoundly wrong.

Consider what happened in the last six years of the 20th century. Stocks tripled, boosting their average historical return. Did it boost expectations for future years? On the contrary, it lowered them; there was less to be gained once prices had gotten ahead of themselves.

My expectations for future returns are based not on past returns but on how many pennies of earnings you get right now for every dollar of capital.

Expected returns

Forbes

Stocks

The S&P 500 index is at 2600; trailing earnings (the weighted average earnings of its components) come to $140. This means a price/earnings ratio of 19 or, equivalently, an earnings yield of 5.4%. That earnings yield is a good starting point for the expected return on stocks.

If corporate earnings kept pace with the cost of living, we could stop right there and have a real return number. Alas, earnings don’t keep up on their own. They need help. Turns out that corporations need to plow back a fourth of their reported net in order to keep their earnings per share constant in inflation-adjusted terms. (I tell more about the arithmetic here.)

Scale back that 5.4% for the necessary reinvestment rate and you get 4%. But even this return may be too much to expect. We’re in the late stages of an economic expansion, and last year’s earnings got an artificial boost from a tax cut. To temper our expectations, let’s use, in place of the trailing earnings number, a five-year average (inflation-adjusted) and then peel off the slice for reinvestment. Now we’re down to 3.2% as the expected real return on U. S. stocks.

You think this is too gloomy? Go to the website maintained by Rob Arnott’s Research Affiliates and select the expectations based on “yield and growth.” For large-company American stocks, RIA expects 3.3%.

“Yield and growth” assumes, like my analysis, constant price/earnings ratios. The firm also reports “valuation dependent” numbers, which posit a collapse of P/Es from their present lofty levels to something more normal. Don’t even look at those; you’ll faint.

Bonds

Calculating the expected return on a high-quality bond is simpler. Start with the yield to maturity and then allow a smidgen for credit losses. That gives you the expected return in nominal dollars. Now subtract your expectation for inflation, and you have an expected real return.

The bonds in the Vanguard Total Bond Market fund have a composite yield to maturity of of 3.25%. This fund is mostly in government-guaranteed paper, so it is reasonable to expect 3.1% for the net return after defaults. Knock off 1.7% for inflation (see below) and you have a 1.4% expected real return.

Inflation

The 20-year Treasury that pays nominal dollars yields 2.9%. The 20-year inflation-protected Treasury yields just over 1%. The 1.9-point spread between these two numbers is a starting point for assessing expected future inflation.

But there’s a risk element at play. The brave people who own nominal bonds are taking on the risk that crazy, 1970s-style inflation will come back. They should be compensated. Perhaps the 1.9 percentage points consist of 1.7 points of expected inflation plus 0.2 points of reward for bearing uncertainty.

There’s debate about the magnitude, and even the sign, of this inflation risk premium. I think it’s a positive number and 0.2 points is a good guess. So I’d say we should clock expected inflation at 1.7%.

An expectation of principal loss arises from several factors. There’s the default rate (roughly 4% in this category historically), the recovery of principal after a default (roughly half historically) and, finally, the poisoning effect of bond calls. Issuers whose prospects improve call in their high-coupon bonds prematurely, leaving investors with a concentrated sludge of weak credits.

Vanguard’s fund is well managed and it avoids the riskiest issues. On the other hand, there has been a lot of investor money flooding into junk in recent years, and corporate borrowers have taken advantage. In a seller’s market, bond buyers wind up with meager protections against having collateral yanked out from underneath their feet.

I’m expecting a 1.9% annual erosion of principal in the Vanguard fund, considerably worse than the fund’s historical number (1.4% since 1979). That takes you down to 4.8%. Subtract inflation at 1.7% and you have a 3.1% expected real return.

Add it up. My expectation for a retirement portfolio that blends stocks and quality bonds with a little bit of junk is an annual purchasing-power return in the neighborhood of 2.5%.

My prediction for 2019 is that you will get something between -50% and +100%.